Half a century ago, Edward Purcell and Norman Ramsey initiated a search for an electric dipole moment (EDM) of the neutron and obtained what was considered at the time a remarkably precise result, consistent with zero. Thus began a long line of ever more sensitive EDM experiments on neutrons, atoms, and molecules. Although no EDM has yet been found, the limits set have had decisive influences on elementary particle theories. Now, experiments under way or being planned may at last find an EDM and, in any event, are expected to have a far‐reaching impact on theoretical particle physics.